Rewrite as a simplified fraction. ${2.75\overline{3} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2753.3333...\\ 100x &= 275.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2478}$ ${x = \dfrac{2478}{900}} $ ${x = \dfrac{413}{150}} \text{or} {2 \dfrac{113}{150}}$